Best strategy for rigging and modelling tongue in face
All the options are equivalent in terms of animation comfort (user interacts with armature only), how they deform (separate or not, the weight painting of vertices can be the same) and materials (you can assign materials to individual faces).

A reason to split your mesh in rigging is to be able to interactively hide parts of it (but this can be also done with mask modifiers on the mesh), or to be able to split it (dismember body parts,..). None apply here.

There are no issues with one armature driving multiple meshes. You can even pack everything up into a group and link it as a single entity with a proxy rig that drives that.

In terms of setting the rig up, having the mesh in one piece is the most convenient, because you have the ability to blend weigh-painting well between bones.